This disclosure deals with systems and methods using a Hermetic Transform, as well as related transforms, for applications such as directional reception and/or transmit of signals using phased-array devices and systems. The Hermetic Transform (and related transforms) can be designed using an array manifold, effectively a complex calibration response vectors from the array in question to signal arrivals from different directions, whether developed from a mathematical model or from collected data, arranged in a particular fashion. The transform can be utilized for receiver and/or transmit beams to provide narrower main-lobes than classical methods would typically allow. Further background about the Hermetic Transform can be found in U.S. Pat. No. 8,064,408, incorporated herein by reference in its entirety and for all purposes.